The sum of the three prime numbers is 100. If one of them exceeds another number by 24, then one of the other numbers is

This question was previously asked in
UPPSC Civil Service 2019 Official Paper 2
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  1. 7
  2. 29
  3. 43
  4. 61

Answer (Detailed Solution Below)

Option 4 : 61
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Let three prime numbers be X, X + 24 and Y.

According to the question,

X + X + 24 +Y = 100

⇒ 2X + Y = 76     ...i)

We can observe that 2X is an even number,

⇒ Y is also an even number

⇒ Y = 2     ...[∵ 2 is only even prime number]

Now, 2X + 2 = 76

⇒ 2X = 74

⇒ X = 37

∴ The three prime numbers are 2, 37, (37 + 24) = 61
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